Looks like you had yourself in some sort off partial-upgrade state and did not manage to fully remove 5.13 or generate proper initramfs …
I am looking for the thread where I walked someone else through it so I dont have to type it again …
OK. Here is a giant one-line command … just copypaste into terminal and hit enter, then share the output:
find /usr/lib/modules -type d -name "*5.13*" 2> /dev/null && find /boot /etc -type f \( -name "*5.13*" -o -name "*513*" \) 2> /dev/null
[edited for a better command for you]
But I am going to guess you will find some 5.13 remnants … that you would then want to remove, like example:
sudo rm /boot/vmlinuz-5.13-x86_64
sudo rm /boot/initramfs-5.13-x86_64.image
sudo rm /boot/initramfs-5.13-x86_64.fallback.image
sudo rm /etc/mkinitcpio.d/linux513.preset
sudo rm -r /usr/lib/modules/extramodules-5.13-MANJARO
sudo rm -r /usr/lib/modules/5.13*
Then reinitialize the things:
sudo mkinitcpio -P
sudo update-grub